DE102011006400B4 - Method for determining the proportion of scattered radiation in 2D X-ray images - Google Patents

Abstract

Method for determining the proportion of scattered radiation reaching an X-ray detector (D) when recording a 2D X-ray image data set of an image object (O), whereby two X-ray image data sets with the same image object (O) while varying the distance (L0, L1) of the X-ray detector (D) are obtained from the image object (O), and the scattered radiation is deduced from each of the two 2D x-ray image data sets, which is reflected in one of the 2D x-ray image data sets, the two respective distances (L0, L1) being selected to match each other that an objective function (F (S0, q ')) becomes minimal, and wherein the objective function is or comprises the ratio of the variance of the scattered radiation at one of the distances to the total primary radiation received when the two 2D x-ray image data sets were obtained.

Description

The invention relates to a method for determining the proportion of scattered radiation reaching an X-ray detector when X-rays are emitted by an X-ray source, namely when recording a 2D X-ray image data set of an image object.

The scattered radiation is that radiation that does not get in a straight line from the X-ray source to the X-ray detector, but in which the X-rays are scattered in the image object, i. H. be deflected in a different direction.

In X-ray imaging with area detectors, the intensity of this scattered radiation, which carries very little image information, can be of the order of magnitude of the intensity of the primary radiation which contains the actual image information. The intensity of the scattered radiation can even be a multiple of that of the primary radiation. This is particularly the case with thorax or abdomen images.

The scattered radiation has negative effects on the quality of an acquired projection image because the contrast in a 2D X-ray image is reduced, the gray value background becomes inhomogeneous and the noise increases. If a tomographic reconstruction is carried out from a plurality of 2D x-ray image data sets, that is to say a 3-D x-ray image data set is calculated, the scattered radiation in the 3-D image data set leads to gray value distortions and artifacts, which significantly affects the image impression.

It is known to at least partially prevent the impact of scattered radiation on the X-ray detector with the aid of an anti-scatter grid. If a particularly large distance is provided between the image object and the X-ray detector, the scattered radiation is also reduced, which is known as the "air gap technology".

In addition to reducing the scattered radiation, efforts are also made to quantify it in order to be able to make corrections in the X-ray images. An example is the article from KP Maher and JF Malone "Computerized scatter correction in diagnostic radiology", Contemporary Physics, 1997, vol. 38, pages 131 to 148, referenced .

It is a constant task of the person skilled in the art to either reduce the proportion of scattered radiation in 2D x-ray image data sets or at least to quantify it as precisely as possible.

The present invention is concerned with the latter alternative. The previous methods for quantifying the portion of scattered radiation that is reflected in a 2D x-ray image data set, that is, makes a contribution to the respective gray values that are assigned to an image point in a 2D raster, are unsatisfactory. The contribution to the gray value can only be given imprecisely. It would be desirable to be able to obtain 2D x-ray image data sets of an image object that have been freed from scattered radiation. This would require the determination of a 2D x-ray image data set of the image object in which only the contributions to the gray values that are based on the scattered radiation are included.

The US 2009/0016593 A1 describes X-ray detectors which are used to determine the relationship between the radiation intensity and the distance between detectors and a radiation source, in order to be able to determine the primary radiation and the scattered radiation separately from one another. Two recordings are obtained with one detector and the distance between the detector and the X-ray source or the image object is selected differently. In order to calculate the ratio of the scattered radiation to the primary radiation, the proportion of the scattered radiation is calculated with a linear function, which is composed of a linear absorption coefficient, a factor based on radius and depth and a factor that depends on the absorption coefficient.

The US 2010/0310037 A1 describes an extraction of a scattering by obtaining two recordings with different image object-detector distances. The data from both images can then be subtracted from one another in order to obtain an estimate of the scattered radiation.

The object of the invention is to make a contribution to solving these problems and, in particular, to provide a method for determining the proportion of scattered radiation when recording a 2D x-ray image that provides results that are as precise as possible. The task also includes providing a method for correcting 2D x-ray image data sets of an image object so that these are freed from the contributions of scattered radiation.

The object is achieved in one aspect with the method according to claim 1, which is used in another aspect in a method for correcting a 2D x-ray image data set according to claim 4 and is the basis for a further procedure there.

In the method according to the invention, two 2D X-ray image data sets are thus obtained for the same image object while varying the distance of the X-ray detector from the image object (in particular with a constant distance between an X-ray source and the image object). The scattered radiation, which is reflected in one of the 2D X-ray image data sets, is then deduced from the two 2D x-ray image data sets. D. H. which has the effect that the gray values in the 2D X-ray image data sets z. B. be increased by a certain contribution at some pixels. The invention is based on the knowledge that the intensity of the primary radiation changes in a different way (namely with an inverse square distance) than the radiation (for which a factor can be specified) when the distance of the X-ray detector from the image object varies. Based on two measurement results, conclusions can be drawn about the two contributions if certain assumptions are made about determinism. Using a suitable mathematical model, the scattered radiation can thus be specified relatively precisely.

Conventional x-ray imaging devices allow the x-ray detector to be placed in different positions that correspond to different distances from the image object, at least to a limited extent. The X-ray source can remain stationary.

The method according to the invention is impressive because of its simplicity, because a second 2D X-ray image can be recorded relatively easily.

The invention thus means that the scattered radiation can be specified precisely or a corresponding correction is made possible.

In this case, the two respective distances are also seen as absolute and, in particular, are chosen to be compatible with one another in such a way that a target function is minimal.

This is based on the knowledge that there are exactly two optimal distances in the underlying mathematical model, at which the measurements (i.e. the acquisition of the 2D X-ray image data sets) are optimally matched to one another in order to enable a good estimate of the scattered radiation. The objective function is the ratio of the variances of the scattered radiation at one of the distances to the total primary radiation measured when the two 2D X-ray image data sets were obtained (“total X-ray dose”), or at least the objective function includes this ratio. This ratio indicates, so to speak, the noise-to-signal ratio, which usually has to be as small as possible so that the contrast is optimal.

In a preferred embodiment of the invention, the x-ray dose emitted by the x-ray source when a 2D x-ray set is obtained is different (selected differently) for the two 2D x-ray image data sets. This is based on the knowledge that, depending on the distance chosen, a higher or lower dose may be desirable. In particular, an envisaged total dose can be divided into two partial doses. Here it proves to be useful if these two partial doses are not necessarily the same size. As a rule, a somewhat higher dose will be selected for that X-ray image data set in which the X-ray detector is located at a greater distance from the image object, because the primary radiation would otherwise have a lower intensity in the 2D X-ray image data set because of the greater distance.

With the method according to the invention, a value for the scattered radiation at a certain distance can be specified in each pixel of the 2D image grid, which is particularly the basis of a 2D image data set, because since measurements are taken at two different distances, two gray values per pixel are available Available from which two quantities, namely the primary radiation and the scattered radiation, can be concluded. A separate 2D (scattered radiation) image data set thus quantifies the scattered radiation.

Correspondingly, it is possible to correct a 2D x-ray image data set in that this 2D image data set is determined and the correction then takes place on the basis of this 2D image data set. In the simplified case, the 2D image data set for the scattered radiation is subtracted from the 2D x-ray image data set which is to be corrected, pixel by pixel. A gray value difference is thus formed.

The invention thus makes it possible to calculate out its influence even in the case of relatively strong scattered radiation, and this on a pixel-by-pixel basis, so that corrected images are available that are higher in contrast and lower in noise than previous images.

• 1 die geometrischen Verhältnisse bei einem ersten Abstand L₀ eines Detektors D von einem Bildobjekt O veranschaulicht und
• 2 die entsprechenden geometrischen Verhältnisse bei einem Abstand L₁ des Detektors D vom Bildobjekt O veranschaulicht.

A preferred embodiment of the invention is described in more detail below with reference to the drawing, in which

• 1 the geometric relationships at a first distance L _{0 of} a detector D. illustrated by an image object O and
• 2 the corresponding geometric relationships at a distance L _{1 from} the detector D. illustrated by image object O.

The core of the present method is that of an image object O with the aid of an X-ray source Q and an X-ray detector D. 2D x-ray image data sets are obtained twice, namely at different distances between the x-ray source Q and X-ray detector D. . In the case of a first X-ray image recording, the distance between the X-ray source is Q and X-ray detector D. A ₀ and the distance between the image object O and the X-ray detector D. L ₀ . In the case of a second X-ray image recording, the distance between the X-ray source is important Q and the X-ray detector D. A ₁ , the distance between the image object O and the X-ray detector D. L ₁ .

With the aid of the X-ray detector, intensity values are obtained for a pixel grid, which are referred to in the present case as T '. The intensity values for the first X-ray image acquisition are designated with T ₀ ', those for the second image acquisition with T ₁ '. The indices 1 and 2 are indicated by the variable k.

The total intensity T _k 'is specified as a function of image points and is made up of components that are due to the primary radiation P _k ' and the scattered radiation S _k '.

In general, the following relationship can be specified: $$T_k\text{'}\left(v_k\underset{\_}{x}\right)=P_k\text{'}\left(v_k\underset{\_}{x}\right)+{\mathrm{S.}}_k\text{'}\left(v_k\underset{\_}{x}\right)$$

The pre-factors v _k result from the central projection with cone beam geometry and are related to the reference distance A ₀ : $$v_k=\left({\mathrm{A.}}_k/{\mathrm{A.}}_0\right)$$

So is $$v_0=1$$

We write the following for the primary intensity (the expected value, i.e. without noise) in the reference detector plane, i.e. for the first X-ray image acquisition: $$P_0\left(x\right):=P_0\text{'}\left(x\right):=P_0\text{'}\left(v_0\underset{\_}{x}\right)$$

The propagation of the primary radiation can be described with the geometric beam optics: accordingly, the primary intensity (per unit area) or the number of photons per detector pixel with a fixed pixel size decreases inversely proportional to the square of the distance A _k , (A _k ) ² , so it applies : $$P_k\text{'}\left(v_k\underset{\_}{x}\right)=P_0\left(\underset{\_}{x}\right){\left({\mathrm{A.}}_0/{\mathrm{A.}}_k\right)}^2=P_0\left(\underset{\_}{x}\right){\left(v_k\right)}^{-2}$$

wobei $$c_k:={\left(v_k\right)}^2$$

If you want to specify the primary radiation for an image point with the coordinates x in the k-th X-ray image, you have to scale back the geometric magnification so that we get: $$P_k\left(\underset{\_}{x}\right):=c_k{P}_k\text{'}\left(v_k\underset{\_}{x}\right)$$

in which $$c_k:={\left(v_k\right)}^2$$

The prerequisite here is that the two measurements are made at different detector distances A ₀ , A ₁ with the same current-time product (i.e. in mAs) of the X-ray tube. Otherwise the factors c _k still have to be corrected.

Solving formula (4) for P ' _k (v _k x ) and inserting the value for c _k according to formula (5) results in formula (3): $$P_k\left(\underset{\_}{x}\right)=P_0\left(\underset{\_}{x}\right)$$

This means nothing else than that the primary intensity distribution in the reference plane A _{0 can} also be obtained by measurements in other detector planes A _k .

The primary intensity is initially unknown, as the scattered radiation is superimposed on it.

$$T_k\left(\underset{\_}{x}\right):=c_k{T}_k\text{'}\left(v_k\underset{\_}{x}\right)$$

In the following, we also take over the defining geometric rescaling and intensity normalization according to the above formula (4) for the scattered radiation and for the total radiation: $${\mathrm{S.}}_k\left(\underset{\_}{x}\right):=c_k{\mathrm{S.}}_k\text{'}\left(v_k\underset{\_}{x}\right)$$

$$T_k\left(\underset{\_}{x}\right):=c_k{T}_k\text{'}\left(v_k\underset{\_}{x}\right)$$

While the propagation of the primary radiation after penetrating the subject can simply be described as a geometric central projection, this is not possible with the scattered radiation scattered in all directions. With increasing distance from the surface of the scattering body (that is, with increasing size of the air gap, indicated by the quantities L ₀ and L ₁ ), the scattered radiation decreases more strongly than the primary radiation. This additional decrease can be described approximately multiplicatively by an empirical factor g _k , which depends on the air gap (and also slightly depends on the size of the scattering body O, on the radiation spectrum and thus on the tube voltage). This is based on the observation that the scattered radiation distribution in the detector plane A _k looks similar to that in the reference plane A ₀ , but its amplitude is reduced by a factor g _k <1, with g ₀ = 1. This approximation using the empirical factors g _k can be written as follows: $${\mathrm{S.}}_k\text{'}\left(v_k\underset{\_}{x}\right)=G_k{\mathrm{S.}}_k\left(\underset{\_}{x}\right)/c_k$$

With (7) it simply applies: $${\mathrm{S.}}_k\left(\underset{\_}{x}\right)=G_k{\mathrm{S.}}_0\left(\underset{\_}{x}\right)$$

In the following, the formulas are given without the dependency on x , as this simplifies the clarity of the formulas. However, the following formulas apply to all x according to the downscaling.

$$P_k+S_k=T_k$$

To estimate the scattered radiation, two equations are available for the entire intensity distribution in the reference plane A ₀ and a second detector plane A _k > A ₀ : $$P_0+{\mathrm{S.}}_0=T_0$$

$$P_k+{\mathrm{S.}}_k=T_k$$

$$P_0+g_k{S}_0=T_k$$

The right-hand sides T ₀ and Tk are given by the two x-ray images, that is to say by measurements. If you put the above formulas (6) and (9) in the formula (10b), you get the formula pair: $$P_0+{\mathrm{S.}}_0=T_0$$

$$P_0+G_k{\mathrm{S.}}_0=T_k$$

You can see that you are only dealing with two unknowns P ₀ , S ₀ , and that you have two determining equations. The two quantities P ₀ and S ₀ can thus be determined.

bzw. für die Streustrahlungsverteilung in der Detektorebene A_k $$S_0^{\#}=g_k{\left(1-g_k\right)}^{-1}\left(T_0-T_k\right)$$

In particular, the unknown primary intensity P ₀ can be eliminated by subtracting (11a) and (11b). It follows for the scattered radiation distribution of the reference plane: $${\mathrm{S.}}_0^{\#}={\left(1-G_k\right)}^{-1}\left(T_0-T_k\right)$$

or for the scattered radiation distribution in the detector plane A _k $${\mathrm{S.}}_0^{\#}=G_k{\left(1-G_k\right)}^{-1}\left(T_0-T_k\right)$$

The # indicates that the sizes are estimates.

It should be remembered again that the factors g _{k are} empirically determined factors. In addition, the named variables can be determined for all x , in this way estimates for the scattered radiation intensities are obtained in the form of “2D image data sets”.

With the aid of formula (11a), after determining the scattered radiation distribution, the scattered radiation-corrected primary intensity distribution can also be determined. Since the estimate (12) can be erroneous and an overcorrection, which could lead to senseless negative primary intensity values, should be avoided, the following under-relaxation formula is used here: $$P_0^{\#}=T_0-\lambda {\mathrm{S.}}_0^{\#}$$

Here A is a factor <= 1 or more generally a location-dependent function of x .

As an alternative to (14a), the primary intensity can also be calculated for the detector plane A _k and later converted to A ₀ by rescaling and intensity normalization: $$P_k^{\#}=T_k-\lambda {\mathrm{S.}}_K^{\#}$$

With exact scatter beam correction, formulas (14a) and (14b) only differ in terms of noise because of the identity (6). In order to reduce the noise and at the same time to use the radiation dose that was applied to the patient by the measurements in the two detector planes for the imaging, it is recommended to average equations (14a) and (14b).

As mentioned above, the same current-time product (mAs) was assumed for the two measurements (x-ray recordings). It was therefore assumed that a total dose with which the image object is applied is half distributed over both measurements. However, it is preferable that the total dose be divided in unequal proportions. To this end, an objective function should first be defined.

This objective function is based on the variance of the scattered radiation.

Namely, in the formula (12), the difference between two quantities containing noise is formed. This difference is also multiplied by a factor that is greater than 1. Therefore, the scattered ray estimation in formula (12) is highly error-prone. By applying the Gaussian error propagation rule and taking into account the Poisson noise Var {P ₀ ) = 〈V〉 (<> here means the statistical expected value) one obtains: $$\begin{array}{cc}Var\left({\mathrm{S.}}_0^{\#}\right)=\left(Var\left(T_0\right)+Var\left(T_k\right)\right)/{\left(1-G_k\right)}^2& \left(\mathrm{15th}\text{a}\right)\\ =\left(<P_0>\left(1+s_0\right)+<P_0>\left(1+s_k\right)\right)/{\left(1-G_k\right)}^2& \left(\mathrm{15th}\text{b}\right).\end{array}$$

s₀=S_0/P₀ und s_k=S_k/P_k=S_k/P₀ sind die jeweiligen Streu-zu-Primärverhältnisse, auf Englisch als „scatter-to-primaryratio“ bezeichnet. g_k kann dann durch $$g_k=s_k/s_0$$

ausgedrückt werden.Hence the formula $$Var\left({\mathrm{S.}}_0^{\#}\right)/<P_0>=\left(2+s_0+s_k\right)/{\left(1-G_k\right)}^2$$

s ₀ = S _{0 /} P ₀ and s _k = S _{k /} P _k = S _{k /} P ₀ are the respective scatter-to-primary ratios, referred to in English as "scatter-to-primaryratio". g _k can then go through $$G_k=s_k/s_0$$

be expressed.

It can be shown here that the variance of the scattered radiation estimated with the formula (12) can be more than 20 times higher for typical values than the variance of the primary radiation would be if it could be measured directly.

For this reason, noise smoothing is carried out before applying formula (12). The noise smoothing can naturally only take place on the overall intensity distributions T ₀ and T _{k in} order to effectively reduce the noise from the start. If the variances of the smoothed intensities T ₀ and T _k are then inserted into equation (15a), the right-hand sides in equations (15b) and (15c) are reduced by a factor γ corresponding to the smoothing. Thus, by modifying the formula (15c), the following formula is obtained $$Var\left({\mathrm{S.}}_0^{\#}\right)/<P>=\gamma \left(2+s_0+s_k\right)/{\left(1-G_k\right)}^2$$

The noise smoothing should be such that the expression reduced by γ in (15) becomes as much smaller than 1 as possible, so that the inevitable noise caused by T ₀ or T _{k is} not significantly increased by the scatter correction in equation (14) . In this way, the increase in noise in the scattered radiation can be reduced from over 20 times to 0.05 times. The increase in noise due to the scatter correction would then be practically negligible.

In the estimation of the scattered radiation distribution according to (12) or (13), the difference T ₀ -T _k is decisive. The “similarity” of the scatter distributions S ₀ and S _k according to formula (9) is also assumed. If this requirement is not met, high-frequency artifacts can occur. To avoid this, a registration can be provided to record T ₀ and T _k z. B. by shifting and equalization so that the artifacts are minimized. In addition, a subsequent low-pass filtering of the difference T ₀ -T _k or also of the scatter distributions estimated with (12) and (13) can be provided.

In the following it should be assumed that the scattered radiation estimation is always based on highly smoothed measurement data.

so erhält man mit (15) die modifizierte Formel: $$Var\left(S_0^{\#}\right)/<P>=\gamma \left(\left(1+s_0\right)/a+\left(1-s_k\right)/\left(1-a\right)\right)/{\left(1-g_k\right)}^2$$

Now that the formula (15) has been specified as a preliminary objective function, it should be modified in such a way that an unequal dose allocation is now also taken into account, i.e. that it is taken into account that a-times the total dose was used in a first image acquisition at distance A ₀ , and at distance A ₁ (1-a) times. If you choose: $$<P_0>=a<P>,<P_k>=\left(1-a\right)<P>,<P>=<P_0>+<P_k>$$

with (15) one obtains the modified formula: $$Var\left({\mathrm{S.}}_0^{\#}\right)/<P>=\gamma \left(\left(1+s_0\right)/a+\left(1-s_k\right)/\left(1-a\right)\right)/{\left(1-G_k\right)}^2$$

Since <P ₀ > has been replaced by the “total dose” <P> in (16), the expression (15) is again obtained at a = 0.5 if the same dose is allocated except for a factor of 2.

You can now choose the size a so that the size V _ar (S ₀ ^# ) / <P> is minimal, or you can choose another objective function based on this function. If one considers z. For example, in the case of noise-limited image quality assessment in low-contrast diagnostics based on the CNR (or SdNR = signal difference-to-noise ratio or detectability index), then in the case without scatter correction, the use of the entire dose for the measurement with a large air gap is optimal. In the case with scattered radiation correction considered here, things are more difficult insofar as the quality gain through the scattered radiation correction has to be assessed in relation to the CNR loss (based on the dose portion assigned to the measurement closer to the object with a larger scattered radiation portion). For applications in which CNR etc. does not play a decisive role (e.g. in material testing), on the other hand, the accuracy of the scattered radiation estimate can be given priority.

$$q=a/\left(1-a\right)$$

After the case has been discussed so far that the dose is different in the two X-ray images, the following should now also be taken into account: The values of the variable VAR S ₀ ^# / <P ₀ > in (15) then become very large because of the quadratic term in the denominator large when g _k = s _k / s _{0 is} close to 1, i.e. when the distance between the two detector planes A _k and A _{0 is} small. Because of the term s ₀ in the numerator, the value also increases the closer the plane A _{0 is to} the object O. The distance between the two detector planes must therefore be as large as possible; on the other hand, the reference plane A _{0 must} not be too close to the object O. There is therefore an optimal configuration. The general error expression (16) is rewritten a bit: it is multiplied by (1-a), divided by γ and the following allocation ratios are introduced: $$q\text{'}=\left(1-a\right)/a$$

$$q=a/\left(1-a\right)$$

wobei F(s₀,q') minimal sein muss. Eine Beschränkung gibt es möglicherweise dadurch, dass es einen maximalen Detektorabstand A_k gibt. Die Lösung der Bedingungsgleichung liefert als optimales s₀, s₀ ^opt $$s_0^{opt}\left(q\right)=\frac{3}{2}{s}_K\left(1+\frac{1}{3}\sqrt{\left(9+8q\right)+8\left(1+q\right)/s_k}\right)$$

und speziell für den Fall der Zuteilung der gleichen Dosis, also q'=q=1: $${s_0^{opt}|}_{q=1}=\frac{3}{2}{s}_K\left(1+\frac{1}{3}\sqrt{17+16/s_K}\right)$$

One thus obtains an objective function for the optimization problem: $$\mathrm{F.}\left(s_0,q\text{'}\right)=\left(\left(1+s_0\right)q\text{'}+1+s_k\right)/{\left(1-s_k/s_0\right)}^2$$

where F (s ₀ , q ') must be minimal. There may be a limitation in that there is a maximum detector spacing A _k . The solution of the conditional equation yields the optimal s ₀ , s ₀ ^opt $$s_0^{Opt}\left(q\right)=\frac{3}{2}{s}_K\left(1+\frac{1}{3}\sqrt{\left(9+\mathrm{8th}q\right)+\mathrm{8th}\left(1+q\right)/s_k}\right)$$

and especially for the case of the allocation of the same dose, i.e. q '= q = 1: $${s_0^{Opt}|}_{q=1}=\frac{3}{2}{s}_K\left(1+\frac{1}{3}\sqrt{\mathrm{17th}+16/s_K}\right)$$

The evaluation of (19a) shows that s ₀ ^opt (q) only weakly depends on q. The air gap L ₀ at which s ₀ ^{opt is} to be expected as the corresponding SPR is determined from s ₀ ^opt , and A ₀ can be derived from this.

If the resulting optimal air gap is too small, so the X-ray detector D. is too close to the image object O, then a somewhat larger distance must be selected, even if it is then only “suboptimal”.

In an even greater generalization of approach (9), a convolution model can be used instead of a multiplication. In the convolution model, the scattered radiation distribution in the detector plane is applied as a scaled and smeared version of the scattered radiation S _{0 of} the reference plane, according to the formula: $${\mathrm{S.}}_k\left(\underset{\_}{x}\right)=G_k**{\mathrm{S.}}_0\left(\underset{\_}{x}\right)$$

$$H_k={\left(I-G_k\right)}^{-1}$$

** means a two-dimensional convolution, and I _k is a two-dimensional convolution kernel to be determined empirically (like the quantities g _k before). Approach (9) is a special case of (20) with G _k = I g _k where I is the unit operator (unit matrix or Dirac delta operator). Analogously to the derivation of (12), the formula (21) and the formula (22) then result for the estimation of the scattered radiation. $${\mathrm{S.}}_0^{\#}=H_k**\left(T_0-T_k\right)$$

$$H_k={\left(\mathrm{I.}-G_k\right)}^{-1}$$

für die Streustrahlungskorrektur d. h. die Schätzung der Primärintensitätsverteilung steht weiterhin die Notwendigkeit starker Glättung bzw. die Vorsichtsmaßnahme entsprechend den obigen Gleichungen (14).The invertibility in (21) is ensured by the fact that the operator norm of G _{k is} less than 1, corresponding to g _k less than 1 in the previous model. In (21), T ₀ and T _{k are} to be understood as already highly smoothed distributions, or the kernel H _k is understood from the outset as a combination of a smoothing two-dimensional convolution kernel according to the formula $$H_k={\left(\mathrm{I.}-G_k\right)}^{-1}Q$$

for the scatter correction, ie the estimation of the primary intensity distribution, there is still the need for strong smoothing or the precautionary measure according to the above equations (14).

It was shown on the basis of formulas that when recording 2D x-ray image data sets, due to the validity of formulas (11a) and (11b), both the scattered radiation and then the primary radiation can be estimated for all (downscaled) x for each x P ₀ can be derived, so a corrected image can be calculated without scattered radiation. The objective function (18) makes it possible to choose an optimal detector distance so that the error in the calculations is particularly small. A suitable distribution of the dose over the two image recordings can also ensure a small error.

Claims (4)

Method for determining the proportion of scattered radiation reaching an X-ray detector (D) when recording a 2D X-ray image data set of an image object (O), two X-ray image data sets with the same image object (O) varying the distance (L ₀ , L ₁ ) of the X-ray detector ( D) are obtained from the image object (O), and the scattered radiation is deduced from each of the two 2D X-ray image data sets, which is reflected in one of the 2D X-ray image data sets, the two respective distances (L ₀ , L ₁ ) matching one another can be selected such that an objective function (F (S ₀ , q ')) becomes minimal, and wherein the objective function is or comprises the ratio of the variance of the scattered radiation at one of the distances to the primary radiation received in total when the two 2D x-ray image data sets were obtained . Procedure according to Claim 1 , characterized in that the x-ray dose emitted by an x-ray source (Q) when a 2D x-ray image data set is obtained is selected differently for the two 2D x-ray image data sets. Method according to one of the preceding claims, characterized in that a 2D image data set is determined which quantifies the scattered radiation. Method for correcting a 2D x-ray image data set, in which a method according to Claim 3 is carried out and the correction is made on the basis of the 2D image data set for the scattered radiation.

Images